Mathematics Education Research Journal最新文献

This study explores variations in prospective teachers’ (PTs’) noticing of students’ mathematical thinking based on narrative writing within the context of a practicum course. The research involved eight PTs, each of whom produced ten weekly narratives throughout the course duration. Most PTs displayed noticing abilities within the average range, with a tendency towards moderate levels, particularly in mixed and focused noticing, as per van Es’s (2011) framework. At the mixed noticing level, PTs predominantly focused on their instructional approaches while also considering learners’ reasoning, albeit with a general perspective. They often made evaluative comments without delving deeply into the specifics that would strengthen their analyses. In contrast, at the focused level of noticing, they dedicated more attention to the specifics of learners’ mathematical reasoning and offered interpretive insights. They cited specific instances and interactions to support their evaluations, demonstrating a more detailed and nuanced engagement with the classroom dynamics. The findings also reveal three distinct profiles of variation in noticing among PTs underscoring the complexity of enhancing noticing skills over time. While profile 1 (average to high levels of noticing) and profile 2 (low to moderate levels of noticing) showed more variation, profile 3 demonstrated a more stable pattern at the moderate levels. These variations might be a result of the bidirectional relationships that exist between the skills of noticing. It could also stem from the events that PTs based their narratives on, affirming that enhancement in noticing is an iterative, context-sensitive process influenced by classroom context and situation awareness.

This study is a systematic review of Technological Pedagogical and Content Knowledge (TPACK) studies concerning primary mathematics education published between 2005 and 2022. The aim of the systematic review was to identify the common features of previous TPACK research on primary mathematics education and identify the research gaps based on their contexts. The study used the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) procedure to investigate TPACK-related studies published during the last 17 years in the primary mathematics education domain and to evaluate the characteristics of TPACK instruments used in primary mathematics education. We identified five foci of these studies of TPACK in primary mathematics education research: designing lessons, evaluating mathematics teachers’ knowledge of integrating digital technologies, designing the assessment, evaluating training programs, and informing professional development program designs. Findings from this systematic review of the literature can assist educators in better designing professional development programs to help primary mathematics teachers improve their ability to integrate digital technology into classroom teaching. Also, the findings can assist researchers in locating TPACK instruments that are appropriate and relevant for their research. Finally, we argue that there is a research gap concerning how to measure primary mathematics teachers’ TPACK, how to design a TPACK instrument that includes contextual factors, and how to develop TPACK-oriented teacher training programs for primary mathematics teachers.

Mathematics education researchers (MERs) use practices unique to the mathematics education discipline to conduct their work. MERs’ practices, i.e., ways of being, interacting, and operating, define the field of mathematics education, are initially learned in doctoral preparation programs, and are encouraged and sanctioned by conferences and publications. Disciplinary practices facilitate MERs’ interactions within mathematics education. When working in interdisciplinary groups, differences in disciplinary ways of being, interacting, and operating can create challenges with completing research and other work. Since MERs’ engagement in interdisciplinary collaborations is encouraged and can result in products contributing to the evolution of the mathematics education discipline, it is important to explore what practices MERs use in interdisciplinary collaborations. We interviewed four MERs who led international interdisciplinary collaborations and used qualitative content analysis to create descriptions of practices described by MERs in their collaborations. Five practices were common between the MERs in interdisciplinary collaborations. MERs conducted interdisciplinary work by using practices that allowed them to situate themselves and others in the group (i.e., being practices), develop ideas (i.e., interacting practices), work towards common goals, and use structures to get the work done (i.e., operating practices). We argue that MERs developed new practices to position themselves and others, interact with practitioners from other disciplines, and get interdisciplinary work done. This study contributes to the evolution of the mathematics education discipline by offering five practices that can orient MERs to conducting interdisciplinary work and discussing how MERs experience interdisciplinary collaborations beyond providing mathematics education expertise.

In our data-driven society, it is essential for students to become statistically literate. A core domain within Statistical Literacy is Statistical Inference, the ability to draw inferences from sample data. Acquiring and applying inferences is difficult for students and, therefore, usually not included in the pre-10th-grade curriculum. However, recent studies suggest that developing a good understanding of key statistical concepts at an early age facilitates the understanding of Statistical Inference later on. This study evaluates the effects of a Learning Trajectory for Statistical Inference on Dutch 9th-grade students’ Statistical Literacy. Theories on informal Statistical Inference and repeated sampling guided the Learning Trajectory’s design. For the evaluation, we used a pre-post research design with an intervention group (n = 267). The results indicated that students made significant progress on Statistical Literacy and on the ability to make inferences in particular, but also on the other domains of Statistical Literacy. To further interpret the learning gains of this group, we compared students’ results with national baseline achievements from a comparison group (n = 217) who followed the regular 9th-grade curriculum, and with international studies using similar test items. Both comparisons confirmed a significant positive effect on all domains of Statistical Literacy. These findings suggest that current statistics curricula for grades 7–9, usually with a strong descriptive focus, can be enriched with an inferential focus.

Abstract

In-service primary school teachers’ professional development and, more specifically, their teacher agency, are analyzed regarding the integration of mathematical education and sustainability. To achieve this, based on semi-structured interviews, several questions involving Education for Sustainable Development (ESD) and links between mathematics education and sustainability are considered, which yielded 44 answers. The analysis of these answers is based on four sub-aspects: knowledge of sustainability and its connection to the SDGs; sustainability practices; links between mathematics education and sustainability; and obstacles and challenges. The results show that teachers exhibit a significant lack of knowledge about sustainability and its connection to the SDGs, making a single association with issues related to the environmental crisis, which is the main focus of the sustainability practices carried out in schools. As pertains to the links between mathematics education and sustainability, most accept the importance of this connection, but point out various obstacles and challenges, such as the lack of knowledge and time, the curriculum itself, and others. It is concluded that it is necessary to design training programs focused on these aspects, in order to contribute to the development of teacher agency, i.e. the appropriation and reconstruction of new resources to face the challenges that mathematics education for sustainability implies in teaching practice.

Abstract

As international focus increasingly turns to the need to build a future mathematics workforce, research has aimed to better understand the salient individual and contextual factors that influence maths engagement and achievement across development. This study investigates self-reported general anxiety, test anxiety, and maths anxiety in two cohorts of Australian students aged 9–10 years (n = 158) and 12–13 years (n = 115) and associations with maths achievement and gender. Test and maths anxiety were negatively correlated with maths achievement and there were no gender differences in maths achievement. Cross-sectional latent profile analyses established two anxiety profiles in the older cohort (low and high across all anxiety measures) and a more complex five-profile solution for the younger cohort (various combinations of anxiety). Members of profiles with higher levels of test and mathematics anxiety had lower maths achievement, with girls over-represented in these profiles.

A theoretical model describing Grade 7 students’ rational number sense was formulated and validated empirically (n = 360), hypothesizing that rational number sense is a general construct consisting of three factors: basic rational number sense, arithmetic sense, and flexibility with rational numbers. Data analysis suggested that rational-number tasks can be categorized based on the validated model. The flexibility component reflects thinking about rational numbers in terms of noticing, using, and expressing relations and properties of numbers in patterns, functions, covariation, and complicated computational tasks. It includes utilizing number structure and relational understanding of operations and numbers. Analysis identified three categories of students that represent different rational-number sense profiles. Category 1 students exhibited a limited basic profile that solved mainly traditional school-based tasks. Category 2 students reflected the basic emergent arithmetic sense profile that responded adequately in operation tasks. Category 3 students represented the flexible emergent profile, as they manipulated underlying structures in a variety of situations, indicating an emergent fundamental shift from an arithmetic to an algebraic focus. A discriminant analysis showed that basic and flexible factors could discriminate students best between the three identified profiles of rational number sense.

Supporting students’ problem-solving skills, solution planning and sequencing of different stages that are involved in successfully developing a meaningful solution to a problem has been a challenge for teachers. This case study was informed by reflective investigation methodology which explored how procedural flowcharts can support student mathematics problem solving in a senior Mathematical Methods subject in Queensland. The paper used thematic analysis to analyse and report on teachers’ perceptions of the utility of procedural flowcharts during problem solving as well as content analysis on how student-developed flowcharts can support their problem-solving skills. Results show that development of procedural flowcharts can support problem solving as it helps with integration of problem-solving stages.

The invention of problems is a fundamental competence that enhances the didactic-mathematical knowledge of mathematics teachers and therefore should be an objective in teacher training plans. In this paper, we revise different proposals for categorizing problem-creation activities and propose a theoretical model for problem posing that, based on the assumptions of the Onto-Semiotic Approach, considers both the elements that characterize a problem and a categorization of different types of problem-posing tasks. In addition, the model proposes a description of the mathematical processes that occur during the sequence of actions carried out when a new problem is created. The model is illustrated by its application to analyze the practices developed by pre-service teachers in three problem-posing tasks aimed at specific didactic-mathematical purposes (mobilizing certain mathematical knowledge or reasoning, contributing to achieving learning goals, or addressing students’ difficulties). We conclude discussing the potential of our model to analyze the mathematical processes involved in problem creation from the perspective of teacher education.

This study draws on quantitative reasoning research to explain how secondary mathematics preservice teachers’ (PSTs) modelling competencies changed as they participated in a teacher education programme that integrated modelling experience. Adopting a mixed methods approach, we documented 110 PSTs’ competencies in Vietnam using an adapted Modelling Competencies Questionnaire. The results show that PSTs improved their real-world-problem-statement, formulating-a-model, solving-mathematics, and interpreting-outcomes competencies. Showing their formulating-a-model and interpreting-outcomes competencies, PSTs enhanced their quantitative reasoning by properly interpreting the quantities and their relationships using different representations. In addition, the analysis showed a statistically significant correlation between PSTs’ modelling competencies and quantitative reasoning. Suggestions for programme design to enhance modelling competencies are included.